A152077 Length of the trajectory of the map x->A003132(x) started at x=n^2 up to the end of its first period.

1, 8, 12, 8, 11, 16, 5, 12, 11, 2, 18, 13, 17, 17, 13, 11, 11, 11, 13, 9, 13, 14, 11, 11, 11, 19, 12, 5, 12, 12, 17, 14, 15, 17, 13, 14, 17, 6, 4, 9, 14, 14, 16, 17, 13, 9, 9, 11, 14, 11, 15, 14, 11, 14, 11, 14, 11, 7, 13, 16, 17, 12, 15, 7, 6, 4, 18, 15, 14, 5, 9, 10, 12, 16, 13, 15, 12, 12

Offset

1,2

Comments

This accumulates the length of the "transient" or "pre-periodic" part of the trajectory started at n^2 plus the length of the first period.

Links

Table of n, a(n) for n=1..78.

Formula

a(n) = A099645(n^2)+A031176(n^2) .

Example

a(5)=11 since the trajectory starting at x=5^2 is 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58 the next term 89 is already there.
a(10)= 2 since the trajectory starting at x=10^2 is 100,1 and the next term is again the 1.
a(11)= 18 because the trajectory is 121, 6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, the next 89 is already there.

Crossrefs

Cf. A031176, A160862.

Sequence in context: A166173 A014453 A160862 * A215696 A325809 A173461

Adjacent sequences: A152074 A152075 A152076 * A152078 A152079 A152080

Keyword

nonn,base

Author

R. J. Mathar, Sep 16 2009

Status

approved